How Can I make the World background Material to be checker Texture?
Use a Checkered texture connected to you world background shader, then just provide it with correct texture coordinates.

From a Texture Coordinate node use the Window coordinate output to get a flat 2D-like background.

Adjust the size with the Checker texture Size parameter, and the proportions with a Mapping node.

They should be relative to the Render Output image aspect ratio you have set in the Render Properties tab. For example if rendering at 1920x1080 you would get $1080/1920=0.5625$